An advanced spatial-unfolding technique capable of reconstructing the activity distribution within an exclusion zone from Compton gamma imager measurements taken outside of it is introduced. Although the method is generally applicable to extended sources, we demonstrate it here on a calibrated Cs-137 point source through Monte Carlo simulation studies as well as with measurements made using a Silicon Compton Telescope for Safety and Security (SCoTSS) gamma imager. For synthetic data the method accurately reconstructs the total activity contained within the mapped zone of interest, even when the size of the basis elements used to reconstruct the activity distribution is larger than the source itself. For experimental data, the method reliably located the source but underestimated its activity by up to 17%. This is accurate enough for real-world security applications. The underestimation is likely due to effects not yet included in the simulated response of the detector. The method has widespread applicability in the radiological/nuclear safety and security field, particularly for scenarios in which a threat material or contaminated area lies within a no-entry or no-fly zone.